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	\textbf{{\Huge Faculty Time Series propagation for encryption algorithms}}
{\center{Dec 25, 2011, 
	Johan Ceuppens, Theo D'Hondt - Vrije Universiteit Brussel}}
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{\large{\textbf{\center Abstract}}}
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\section{\large Introduction}

According to Key algorithms for time series encytption and decryption there 
are several series involved. For the fastest series faculty is in order.
Most functional analysis and algebra uses Taylor or MAclaurin Series to develop
a pattern or Shrodinger equation's solutions. For coevolution on NK(d) models
we get extra parameters en surplus of the NK inputs and outputs. 
Co-evolution can only become an eq. with more solutions if the entropy of these
gets very extensive. Most parameters in embryological (NKd) algorithms are
dependent on a function which also can be a faculty. 

\section{\large Extensive Axis Evolutionary Series}

To have an extensive cloud of extrema in fitness evaluation of solution spaces
and not using Lagrangians to convert between solutions (thus not using an
Support Vector Machine) you must have a high number of solutions for high entropy
and much chaos in the attractor-rich vector space. If one would extend a
solution space's axes by e.g. using more parameters or a true random function
which uses irratioanlity of numbers to develop its own algebraic number system
you get more data dependent on more coordinates which yield more numbers, more
solutions.

Faculty can be brought in in each of these systems to have large numbercrunchers
 display more data. Most series are Taylor derivatives because of inner 
funcionality (each and every function yields a Taylor series) which is of
the form $(Taylor Series)$ with faculty in the -noemer- and powers in the 
-teller-. If one would develop a faculty in the -teller- functional propagation
it would have more solutions yielded faster and with more entropy though not 
with and for every function derived in this series.

\section{\large Entropy}

Multiple tuple (e.g. 10 dimensions) are all dependent on axes which
are orthonormal on each other (even if this is goniomtricallly impossible)
so yield higher entropy because of wider solution space.

\section{\large FPGA electronics}

By using FPGAs for developing the electronical faculty time series coordinated
with evolution, input-outputs (NK); boolean networks can bring forth
this system. For each axis an FPGA has multiple possibilities by developing
a 3-dimensional curveand can be combined in multi processing hardware.

\section{\large Conclusion}

Try to find faculty convolutions, analysis, series or entropy functions and so
on. Power series are easily derived using MAclaurin-Taylor series but faculty
has somewhat been left behind. That's it.

\bibliographystyle{plain}
\bibliography{refs} % refs.bib

%Ph. D. P. van Remortel - VUB 

%Cybernetics 2nd ed. - N. Wiener

%M. thesis - Johan Ceuppens

%Orgins of Order - book Kauffman

%Graphics Gems 123 - book

%Neural Computers - book

%article Zhou
%article Savvides 
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